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FrodoKEM

Practical quantum-secure key encapsulation from generic lattices

About FrodoKEM

FrodoKEM is a family of key-encapsulation mechanisms that are designed to be conservative yet practical post-quantum constructions whose security derives from cautious parameterizations of the well-studied learning with errors problem, which in turn has close connections to conjectured-hard problems on generic, algebraically unstructured lattices.

Standardization

FrodoKEM is standardized by ISO as part of ISO/IEC 18033-2:2006/Amd 2:2026, Information technology — Security techniques — Encryption algorithms — Part 2: Asymmetric ciphersAmendment 2.

FrodoKEM has been submitted as an Internet-Draft to the Internet Research Task Force's Crypto Forum Research Group for consideration for standardization.

FrodoKEM was selected as a "Round 3 alternate candidate" in the NIST Post-Quantum Cryptography Standardization project, but was not selected for standardization.

FrodoKEM, at level 3 and 5, is one of two post-quantum algorithms recommended by the German Federal Office for Information Security (BSI) as cryptographically suitable for long-term confidentiality, and is also recommended for use by the European Union Agency for Cybersecurity.

Algorithm information

FrodoKEM is designed for IND-CCA security at three levels:

FrodoKEM-640, which targets Level 1 in the NIST call for proposals (matching or exceeding the brute-force security of AES-128),
FrodoKEM-976, which targets Level 3 in the NIST call for proposals (matching or exceeding the brute-force security of AES-192),
FrodoKEM-1344, which targets Level 5 in the NIST call for proposals (matching or exceeding the brute-force security of AES-256).

FrodoKEM consists of two variants determined on whether there is key reuse: a standard variant that does not impose any restriction on the reuse of key pairs, and an ephemeral variant (eFrodoKEM) that requires the generation of a fresh key pair after a fairly small number (e.g., 2^8) of protocol executions.

For each security level and variant, there is a choice of the symmetric primitive used in one step of the protocol:

FrodoKEM-640-AES, FrodoKEM-976-AES, and FrodoKEM-1344-AES, and eFrodoKEM-640-AES, eFrodoKEM-976-AES, and eFrodoKEM-1344-AES, which use AES-128 to pseudorandomly generate a large public matrix (A).
FrodoKEM-640-SHAKE, FrodoKEM-976-SHAKE, and FrodoKEM-1344-SHAKE, and eFrodoKEM-640-SHAKE, eFrodoKEM-976-SHAKE, and eFrodoKEM-1344-SHAKE, which use SHAKE128 to pseudorandomly generate the matrix.

The AES variants are particularly suitable for devices having AES hardware acceleration (such as AES-NI on Intel platforms), while the SHAKE variants generally provide competitive or better performance in comparison with the AES variants in the absence of hardware acceleration.

Team

The FrodoKEM team consists of:

Erdem Alkim
Joppe W. Bos, NXP Semiconductors
Léo Ducas, CWI
Lewis Glabush, EPFL
Patrick Longa, Microsoft Research
Ilya Mironov
Michael Naehrig, IonQ
Valeria Nikolaenko
Chris Peikert, University of Michigan
Ananth Raghunathan
Douglas Stebila, University of Waterloo
Fernando Virdia, University of Surrey

Additional submitters for the FrodoKEM NIST submission are:

Karen Easterbrook, Microsoft Research
Brian LaMacchia

FrodoKEM builds on an extensive line of literature which is detailed in the specification.

You can contact the FrodoKEM team by emailing [email protected].

Specification

The current versions of the FrodoKEM specification are:

ISO specification ISO/IEC 18033-2:2006/Amd 2:2026

FrodoKEM Internet-Draft

Paper

The most recent version of the academic paper describing FrodoKEM is the IACR Communications in Cryptology volume 2025 issue 3 paper (or the equivalent eprint).

Code

We make available:

a reference implementation written exclusively in portable C,
an optimized implementation written exclusively in portable C that includes efficient algorithms to generate the matrix A and to compute the matrix operations AS + E and S'A + E',
an additional, optimized implementation for x64 platforms that exploits Advanced Vector Extensions 2 (AVX2) intrinsic instructions, and
a extensively commented reference implementation written exclusively in Python 3.

The implementations support all twelve schemes: FrodoKEM-640-AES, FrodoKEM-640-SHAKE, FrodoKEM-976-AES, FrodoKEM-976-SHAKE, FrodoKEM-1344-AES, and FrodoKEM-1344-SHAKE, and eFrodoKEM-640-AES, eFrodoKEM-640-SHAKE, eFrodoKEM-976-AES, eFrodoKEM-976-SHAKE, eFrodoKEM-1344-AES, and eFrodoKEM-1344-SHAKE. The only difference between the reference and the optimized implementation is that the latter includes two efficient functions to generate the public matrix A and to compute the matrix operations AS + E and S'A + E'. Similarly, the only difference between the optimized and the additional implementation is that the latter uses AVX2 intrinsic instructions to speed up the implementation of the aforementioned functions. Hence, the different implementations share most of their codebase: this illustrates the simplicity of software based on FrodoKEM.

All our implementations avoid the use of secret address accesses and secret branches and, hence, are protected against timing and cache attacks.

View FrodoKEM code on GitHub

Previous documents

Internet-Draft (March, 2026)

FrodoKEM Internet-Draft – 2026/03/18

IACR Communications in Cryptology paper (October, 2025)

Preliminary Standardization Proposal (September, 2025)

FrodoKEM Preliminary Standardization Proposal – 2025/09/29 (PDF)

Internet-Draft (March, 2025)

FrodoKEM Internet-Draft – 2025/03/17

Preliminary Standardization Proposal (December, 2024)

FrodoKEM Preliminary Standardization Proposal – 2024/12/05 (PDF)

Preliminary Standardization Proposal (March/April, 2023)

June 4, 2021 update

FrodoKEM Round 3 specification – 2021/06/04 (PDF)

NIST Round 3 submission (September 30, 2020)

March 25, 2020 update

July 2, 2019 update

NIST Round 2 submission (March 30, 2019)

NIST Round 1 submission (November 30, 2017)

Pre-NIST

"Frodo: Take off the ring! Practical, quantum-secure key exchange from LWE" In Proc. 23rd ACM Conference on Computer and Communications Security (CCS) 2016 (PDF)

Third-party implementations

FrodoKEM in Go, by Eduardo Riccardi
FrodoKEM in Go via Cloudflare's CIRCL library, by Goutam Tamvada
FrodoKEM in C++ as a header-only library, by Anjan Roy
Botan, a C++ cryptography library

News

December 16, 2019: Tagesspiegel Background: "Informationssicherheit im Quantenzeitalter" – Arne Schönbohm, President of the Bundesamt für Sicherheit in der Informationstechnik (BSI), announces that FrodoKEM will be recommended by BSI as one of two key exchange methods that are 'fundamentally suitable (in hybrid solutions)'.
July 22, 2020: NIST Round 3 Candidates – FrodoKEM is selected by NIST as a Round 3 "alternate candidate".
August 24, 2020: Post-Quanten-Kryptografie: Update der Handlungsempfehlungen – Germany's Bundesamt für Sicherheit in der Informationstechnik (BSI) continues to recommend FrodoKEM for providing post-quantum confidentiality.
March 31, 2021: BSI TR-02102-1 "Cryptographic Procedures: Recommendations and Key Lengths" Version: 2021-01: BSI recommendation for use of FrodoKEM for post-quantum confidentiality.
January 18, 2022: Prepare for the threat of quantumcomputers – The Netherlands National Communications Security Agency (NLNCSA) recommends FrodoKEM to achieve post-quantum confidentiality.
July 5, 2022: NIST PQC Standardization Process: Announcing Four Candidates to be Standardized, Plus Fourth Round Candidates – FrodoKEM is not selected by NIST for standardization or Round 4. Congratulations to the Kyber team and the candidates proceeding to Round 4.
October, 2022: ISO/IEC JTC 1/SC 27/WG 2 establishes a preliminary work item to consider standardization of FrodoKEM.
April, 2023: ISO/IEC JTC 1/SC 27/WG 2 has agreed to move forward with the standardization of FrodoKEM as an approved mechanism in a revision of ISO/IEC 18033-2, Encryption algorithms — Part 2: Asymmetric ciphers.
March, 2025: FrodoKEM submitted to IRTF Crypto Forum Research Group (CFRG) as an Internet-Draft.
October, 2025: A paper reflecting the current status of FrodoKEM (including post-NIST updates such as salting and refreshed parameter analysis) is published in the IACR Communications in Cryptology.
June, 2026: FrodoKEM is standardized by ISO as part of ISO/IEC 18033-2:2006/Amd 2:2026
June 2026: FrodoKEM is one of two post-quantum KEMs recommended for use by the European Union Agency for Cybersecurity (version 3 draft as of June 2, 2026)